> On 24 Mrz., 20:57, fom <fomJ...@nyms.net> wrote:> > > > Please answer this question (the best way for our readers to> > > understand the difference between pot. and act. infinity):> > > What is the difference between the Binary Tree that constains only all> > > finite paths and the Binary Tree that contains in addition all> > > actually infinite paths?> >> > The first does not exist.> > Another interesting opinion. But why does it not exist?

Either the tree is not a binary one, or it will necessarily contain at least one infinite path

Here is the schematic for a binary tree with one and only one path of each positive finite length.

Note that it also and necessarily has an infinite path of 0 nodes.

Root | \ 0 1 | \ 0 1 | \ 0 1 | \ 0 1 | \ 0 1 | \ 0 1 | \ 0 1 | \ 0 1

and so on, ad infinitum, each 0 node having two children and each 1 having none.--